Collected Works

This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.

Collected Works

Description

Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past. This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.

Collected Works

Table of Contents

1. Introductory Note to 1938, 1939 and 1940, Robert M. Solovay2. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis3. Consistency Proof for the Generalized Continuum Hypothesis 4. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory5. Introductory Note to 1946, Charles Parsons6. Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics7. Introductory Note to 1947 and 1964, Gregory H. Moore8. What is Cantor's Continuum Problem?9. Introductory Note to 1949 and 1952, S.W. Hawking10. An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation11. A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy12. Rotating Universes in General Relativity Theory13. Introductory Note to 1958 and 1972, A.S. Troelstra14. On a Hiterto Unutilized Extension of the Finitary Standpoint16. What is Cantor's Continuum problem?17. On an Extension of Finitary Mathematics Which has not Yet Been Used18. Some Remarks on the Undecidability Results19. Introductory Note to 1974, Jens E. Fenstad20. Remark on Non-Standard Analysis

Collected Works

Author Information

The Editor-in-Chief Solomon Feferman is Professor of Mathematics and Philosophy, and Chairman of the Department of Mathematics at Stanford University. He is past president of the Association of Symbolic Logic.

The Editors John W. Dawson, Jr., is Professor of Mathematics at Pennsylvania State University, York. Steven C. Kleene is Emeritus Dean of Letters and Science, and Emeritus Professor of Mathematics and Computer Science at the University of Wisconsin, Madison. Gregory H. Moore is Associate Professor of Mathematics at McMaster University, Hamilton, Ontario, Canada. Robert M. Solovay is Professor of Mathematics at the University of California, Berkeley. The late Jean van Heijenoort was Emeritus Professor of Philosophy at Brandeis University until his death in 1986.

Collected Works

Reviews and Awards

"I was initially inspired for this review when I happened to pick up Volume 2 of Kurt Godel's Collected Works: anyone with a serious interest in the intellectual history of the 20th century should do the same. Godel's famous proof of the incompleteness of arithmetic is arguably the most famous theorem of our century . . . . These volumes are intended for the mainstream and they succeed admirably; Solomon Feferman and his distinguished board of editors have produced a collected works that is a model for all such endeavors. The collection is beautifully designed; I congratulate Oxford University Press on the high quality with which every detail is executed. Papers originally written in German are translated on facing pages, and it really is "complete" . . . . The introductory material is profuse and worth the price on its own . . . . Godel was a meticulous writer, and with some excellent editorial handling, the proof is a pleasure to read." --A.I. Expert